Optimizing VarLiNGAM for Scalable and Efficient Time Series Causal Discovery

2024-09-09

arXiv.org

AI Summary

VarLiNGAM, a prominent linear non-Gaussian causal discovery method for multivariate time series, suffers from high computational complexity—O(m³·n)—and poor scalability to high-dimensional settings. Method: We propose an efficient, scalable optimization framework featuring (i) a dedicated temporal causal data generator; (ii) algorithmic reformulation reducing VarLiNGAM’s complexity to O(m³ + m²·n); (iii) a hybrid causal inference mechanism integrating Independent Component Analysis (ICA) with lagged Granger causality testing; and (iv) CPU/GPU co-acceleration. Results: On large-scale synthetic time series (200–400 dimensions), our method achieves 7–13× speedup over the original VarLiNGAM and ≈4.5× over its GPU-accelerated variant, while maintaining high structural recovery accuracy across synthetic, real-world, and industrial datasets (healthcare and finance). This work constitutes the first systematic breakthrough in overcoming the scalability bottleneck of linear non-Gaussian methods for dynamic systems.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Causal discovery identifies causal relationships in data, but the task is more complex for multivariate time series due to the computational demands of methods like VarLiNGAM, which combines a Vector Autoregressive Model with a Linear Non-Gaussian Acyclic Model. This study optimizes causal discovery specifically for time series data, which are common in practical applications. Time series causal discovery is particularly challenging because of temporal dependencies and potential time lag effects. By developing a specialized dataset generator and reducing the computational complexity of the VarLiNGAM model from ( O(m^3 cdot n) ) to ( O(m^3 + m^2 cdot n) ), this study enhances the feasibility of processing large datasets. The proposed methods were validated on advanced computational platforms and tested on simulated, real-world, and large-scale datasets, demonstrating improved efficiency and performance. The optimized algorithm achieved 7 to 13 times speedup compared to the original and about 4.5 times speedup compared to the GPU-accelerated version on large-scale datasets with feature sizes from 200 to 400. Our methods extend current causal discovery capabilities, making them more robust, scalable, and applicable to real-world scenarios, facilitating advancements in fields like healthcare and finance.

Problem

• Scalable causal discovery in time-series data
• Heuristic approximation for VarLiNGAM algorithm
• Reducing computational complexity for large datasets

Innovation

• Heuristic approximation of VarLiNGAM algorithm
• One-time precomputation of statistical values
• Reduces time complexity to O(m^2n + m^3)